Binary completely reachable automata

TL;DR

This paper characterizes a special class of complete deterministic finite automata with two input letters, where every non-empty subset of states can be reached from the entire state set, and provides an efficient recognition algorithm.

Contribution

It offers a novel characterization and a polynomial-time algorithm for recognizing binary automata with complete reachability properties.

Findings

Characterization of completely reachable automata with two input letters

Polynomial-time recognition algorithm for this class

Insight into the structure of automata with full subset reachability

Abstract

We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a polynomial-time algorithm for recognizing this class of automata.